Question

exit ticket #2.6
learning target: i can tell whether two expressions are equivalent and explain why or why not.
a cardboard box, which weighs 0.6 pounds when empty, is filled with 15 bags of beans and a 4 - pound bag of rice. the total weight of the box and the contents inside it is 25.6 pounds. one way to represent this situation is with the equation 0.6 + 15b+4 = 25.6.

1. in this situation, what does the solution to the equation represent?
2. circle all equations that are also equivalent to 0.6 + 15b + 4 = 25.6.

equation a: 15b + 4 = 25.6
equation b: 15b + 4 = 25
equation c: 3(0.6 + 15b + 4)=76.8
equation d: 15b = 25.6
equation e: 15b = 21
criteria for mastery: students provide a reasonable explanation of the solution to an equation and identify at least two equivalent equations.
mastered? circle one: yes (advance to next lesson) no (revise practice work, then reassess)

Explanation:

Step1: Analyze the equation's meaning

The equation $0.6 + 15b+4 = 25.6$ represents the total - weight situation. Here, $0.6$ is the weight of the empty box, $15b$ is the total weight of 15 bags of beans (where $b$ is the weight of one bag of beans), and $4$ is the weight of the bag of rice. The solution for $b$ in the equation will give the weight of one bag of beans.

Step2: Check equivalent equations

For Equation A: Subtracting $0.6$ from both sides of $0.6 + 15b + 4 = 25.6$ gives $15b + 4=25.6 - 0.6=25$, not $25.6$, so Equation A is not equivalent.
For Equation B: Subtracting $0.6$ from both sides of $0.6 + 15b + 4 = 25.6$ gives $15b + 4 = 25$, so Equation B is equivalent.
For Equation C: Multiply both sides of $0.6 + 15b + 4 = 25.6$ by $3$. The left - hand side is $3(0.6 + 15b + 4)$ and the right - hand side is $3\times25.6 = 76.8$, so Equation C is equivalent.
For Equation D: Subtracting $0.6$ and $4$ from the left - hand side of $0.6 + 15b + 4 = 25.6$ gives $15b=25.6-(0.6 + 4)=21$, not $25.6$, so Equation D is not equivalent.
For Equation E: Subtracting $0.6$ and $4$ from both sides of $0.6 + 15b + 4 = 25.6$ gives $15b=25.6-(0.6 + 4)=21$, so Equation E is equivalent.

Answer:

1. The solution of the equation represents the weight of one bag of beans.
2. Equation B: $15b + 4 = 25$

Equation C: $3(0.6 + 15b + 4)=76.8$
Equation E: $15b = 21$